A consumer group is investigating two brands of popcorn, R and S. The percent of kernels that will pop for the population of kernels in Brand R is 90% (PK - 0.90). The percent of kernels that will pop for the population of kernels in Brand S is 85% (ps = 0.85). Two independent random samples were taken from the population. The following table shows the sample statistics. Number of Kernels in Samples Proportion from Sample that Popped
Brand R 100 0.92
Brands 200 0.89

Consider the sampling distribution for the difference in all samples of size 100 kernels from Brand Rand 200 kernels from Brand S (Brand R - Brand S). A consumer group claims that the difference in proportions has a mean of 0.03. Is this correct?